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One-sided Markov additive processes with lattice and non-lattice increments

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  • Ivanovs, Jevgenijs
  • Latouche, Guy
  • Taylor, Peter

Abstract

Dating from the work of Neuts in the 1980s, the field of matrix-analytic methods has been developed to analyse discrete or continuous-time Markov chains with a two-dimensional state space in which the increment of a level variable is governed by an auxiliary phase variable. More recently, matrix-analytic techniques have been applied to general Markov additive models with a finite phase space. The basic assumption underlying these developments is that the process is skip-free (in the case of QBDs or fluid queues) or that it is one-sided, that is it is jump-free in one direction.

Suggested Citation

  • Ivanovs, Jevgenijs & Latouche, Guy & Taylor, Peter, 2025. "One-sided Markov additive processes with lattice and non-lattice increments," Stochastic Processes and their Applications, Elsevier, vol. 190(C).
    • Handle: RePEc:eee:spapps:v:190:y:2025:i:c:s0304414925002157
    DOI: 10.1016/j.spa.2025.104771
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    References listed on IDEAS

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    1. Andreas E. Kyprianou, 2006. "Introductory Lectures on Fluctuations of Lévy Processes with Applications," Springer Books, Springer, number 978-3-540-31343-4, August.
    2. A. B. Dieker & M. Mandjes, 2011. "Extremes of Markov-additive Processes with One-sided Jumps, with Queueing Applications," Methodology and Computing in Applied Probability, Springer, vol. 13(2), pages 221-267, June.
    3. Zbigniew Palmowski & Lewis Ramsden & Apostolos D. Papaioannou, 2024. "Exit Times for a Discrete Markov Additive Process," Journal of Theoretical Probability, Springer, vol. 37(2), pages 1052-1078, June.
    4. D'Auria, Bernardo & Kella, Offer & Ivanovs, Jevgenijs & Mandjes, Michel, 2010. "First passage of a Markov additive process and generalized Jordan chains," DES - Working Papers. Statistics and Econometrics. WS ws103923, Universidad Carlos III de Madrid. Departamento de Estadística.
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